JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 26 June 2022, Shift 2, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :

(1) $10$
(2) $36$
(3) $43$ Official answer
(4) $60$

Official answer

Option 3

NTA final key.

Chapter: Statistics
Topic: Variance and SD
Idea tested: Correcting Incorrect Variance

Same idea in other shifts

Asked 10× in all

7 Apr 2025, Shift 1 · Q9The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40.…EasySingle correct
6 Apr 2024, Shift 1 · Q18The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation…EasySingle correct
8 Apr 2023, Shift 2 · Q18Let the mean and variance of 12 observations be $\frac{9}{2}$ and $4$ respectively. Later on, it was observed that two observations were…MediumSingle correct
13 Apr 2023, Shift 2 · Q29The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks…EasyNumerical value
15 Apr 2023, Shift 1 · Q19The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded…EasySingle correct
27 Jul 2022, Shift 1 · Q22The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for…EasyNumerical value
28 Jun 2022, Shift 1 · Q23The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the…EasyNumerical value
26 Aug 2021, Shift 1 · Q80The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.